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A262965
Least number k such that k mod s = prime(n) where s is the sum of the distinct primes dividing k.
2
12, 10, 14, 15, 26, 57, 38, 85, 87, 62, 111, 129, 86, 603, 159, 177, 122, 201, 219, 146, 237, 927, 267, 545, 309, 206, 327, 218, 1057, 1016, 1359, 411, 278, 1267, 302, 471, 489, 3088, 519, 537, 362, 1561, 386, 597, 398, 1687, 3856, 687, 458, 1897, 717, 482
OFFSET
1,1
COMMENTS
Conjecture: a(n) exists for all n > 0.
Many terms are numbers with two distinct prime divisors, exceptions being a(157) = 15465, a(254) = 25815, a(279) = 28695, a(303) = 31665, ... which have three prime distinct divisors, ...
LINKS
EXAMPLE
a(5) = 26 because 26 = 2*13 => 26 mod (2+13) = 26 mod 15 = 11 = prime(5).
MATHEMATICA
Table[k=1; While[Mod[k, Plus@@First[Transpose[FactorInteger[k]]]]!=Prime[n], k++]; k, {n, 50}]
PROG
(PARI) spf(k) = my(f = factor(k)); vecsum(f[, 1]);
a(n) = {k=2; while (k % spf(k) != prime(n), k++); k; } \\ Michel Marcus, Oct 06 2015
(Python)
from sympy import prime, primefactors
def a(n):
k, target = 2, prime(n)
while k%sum(primefactors(k)) != target: k += 1
return k
print([a(n) for n in range(1, 53)]) # Michael S. Branicky, Dec 10 2021
CROSSREFS
Cf. A008472.
Sequence in context: A109683 A140267 A343530 * A094450 A307166 A297910
KEYWORD
nonn
AUTHOR
Michel Lagneau, Oct 05 2015
STATUS
approved